VH-HYC was under the control of Melbourne Sector one on track from Oodnadatta to Woomera cruising at Flight Level (FL) 380. The pilot requested a climb to FL390. The aircraft was cleared to FL390 but the coordination of level change was not passed onto Adelaide Control which was the next controlling authority. The sector controller advised that there was more than 15 minutes to the adjoining airspace boundary when the aircraft requested a climb which meant he did not have to coordinate with Adelaide Control prior to approving the level change. He believes that he cocked the VH-HYC flight strip as a reminder to coordinate with Adelaide after approving the level change. It is possible that while processing two other flight strips, he may have inadvertently knocked the strip for VH-HYC back into its normal position thereby removing his memory cue for the need to coordinate with Adelaide. Air Traffic Services (ATS) management personnel have subsequently formalised a procedure for marking flight strips which should facilitate scanning techniques and help guard against items being overlooked. Significant Factors The following factors were considered relevant to the development of the incident: 1. The controller probably inadvertently lost his reminder cue to coordinate the aircraft's change of level with Adelaide ATS.